Categories Around the Breakpoints: A Weapon Guide

Gratuitous Forum Gratuitous Modding
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Introduction
A work in progress.

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Breakpoints and their implications

GSB has 3 major types of breakpoints

  1. Shield Resistance vs Shield Penetration (SP)
  2. Armor Resistance vs Armor Penetration (AP)
  3. Speed vs Tracking Speed (TS)

Implications:

A weapon is low-SP if it’s < 10 (cannon break shields)
A weapon is mid-SP if it’s >= 10 but < 27 (breaks frigate shields)
A weapon is high-SP if it’s >= 27 (breaks cruiser shields)

A weapon is low-AP if it’s < 20 (breaks no armor)
A weapon is mid-AP if it’s >= 20 but < 60 (breaks armor intended for AA)
A weapon is high-AP if it’s >= 60 (breaks armor tanks)

A weapon is non-TS if it’s < 0.5 (hits non moving)
A weapon is low-TS if it’s >= 0.5 but < 1 (hits moving cruisers)
A weapon is mid-TS if it’s >= 1 but < 2.5 (hits moving frigates)
A weapon is high-TS if it’s >= 2.5 (hits fighters)

Note plasma has reduced chance to hit despite it’s tracking.

This creates 36 combination for weapons

low-SP low-AP non-TS
low-SP low-AP low-TS
low-SP low-AP mid-TS
low-SP low-AP high-TS (anti fighters)

low-SP mid-AP non-TS
low-SP mid-AP low-TS
low-SP mid-AP mid-TS
low-SP mid-AP high-TS (anti fighters)

low-SP high-AP non-TS (anti tank)
low-SP high-AP low-TS (anti tank)
low-SP high-AP mid-TS (anti tank)
low-SP high-AP high-TS (anti tank, anti fighters)

mid-SP low-AP non-TS
mid-SP low-AP low-TS
mid-SP low-AP mid-TS (anti frigates)
mid-SP low-AP high-TS (anti frigates, anti fighters)

mid-SP mid-AP non-TS
mid-SP mid-AP low-TS
mid-SP mid-AP mid-TS (anti frigates)
mid-SP mid-AP high-TS (anti frigates, anti fighters)

mid-SP high-AP non-TS (anti tank)
mid-SP high-AP low-TS (anti tank)
mid-SP high-AP mid-TS (anti tank, anti frigates)
mid-SP high-AP high-TS (anti tank, anti frigates, anti fighters)

high-SP low-AP non-TS
high-SP low-AP low-TS (anti cruisers)
high-SP low-AP mid-TS (anti cruisers, anti frigates)
high-SP low-AP high-TS (anti cruisers, anti frigates, anti fighters)

high-SP mid-AP non-TS
high-SP mid-AP low-TS (anti cruisers)
high-SP mid-AP mid-TS (anti cruisers, anti frigates)
high-SP mid-AP high-TS (anti cruisers, anti frigates, anti fighters)

high-SP high-AP non-TS (anti tank)
high-SP high-AP low-TS (anti tank, anti cruisers)
high-SP high-AP mid-TS (anti tank, anti cruisers, anti frigates)
high-SP high-AP high-TS (anti tank, anti cruisers, anti frigates, anti fighters)

Not all combination serves a purpose. Those with no roles tend to be uninteresting, those with too much roles might be too universal for a strategy game. Therefore, by looking at only those with 1 - 2 roles, we now have 19 combination. which can be broken down into 5 categories.

Anti Tank

low-SP high-AP non-TS
low-SP high-AP low-TS
low-SP high-AP mid-TS

mid-SP high-AP non-TS
mid-SP high-AP low-TS (Proton Beam)

high-SP high-AP non-TS

Anti Cruiser

high-SP low-AP low-TS (Cruiser Laser)
high-SP mid-AP low-TS (MWM, Cruiser Fast Missiles, Cruiser Plasma)

Anti Frigate

mid-SP low-AP mid-TS
mid-SP mid-AP mid-TS (Frigate Beam Laser)

Anti Fighters

low-SP low-AP high-TS (Defense Laser, Anti Fighter Missiles)
low-SP mid-AP high-TS

Dual Roles

mid-SP low-AP high-TS (anti frigates, anti fighters)
mid-SP mid-AP high-TS (anti frigates, anti fighters) (Pulse Laser)

high-SP low-AP mid-TS (anti cruisers, anti frigates) (Ion Cannon)
high-SP mid-AP mid-TS (anti cruisers, anti frigates) (Rad Gun)

low-SP high-AP high-TS (anti tank, anti fighters)
mid-SP high-AP mid-TS (anti tank, anti frigates) (Cruiser Beam Laser, Fusion Beam)
high-SP high-AP low-TS (anti tank, anti cruisers)

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Range

Range can be broken down into 4 types, they are

Short Range (SR), with range > 600
Mid Range (MR), with range >=600 but < 900
Long Range (LR), with range >= 900 but <= 1200
Super Long Range (SLR), with range > 1200

Typically I will advise against weapon with SLR, they tend to kill diversity more than add while severely upset the balance of this game. So they will NOT be included in this guide.

When combined with breakpoints combination, we now has 57 different combination of weapons (19x3).
Or if we look at as categories, we now have 15 types of weapons (5*3).

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Putting in Numbers

True Cost of Damage

Weapon module has 3 basic cost

Credit
Power
Crew

And provides 2 benefits

Damage
HP

To find the true cost of damage, we need to convert power and crew cost into credit.

Each Credit is worth 2.2 HP.
We know this empirically because reinforced crews are used in competitive play. The difference in cost between a reinforced crew and crew 2 is 55, while the difference in HP is 25. 55/25 = 2.2

Each Crew is worth 0.2 credits
Assuming perfect efficiency, we can
take the most efficient crew (micro crew)
take away it’s HP cost (50 - (75/2.2)) = 15.9
divided by total crew (15.9/80) = 0.2

Each Power is worth 2.32 credits
Assuming perfect efficiency, we can
take the most efficient power plant (power 1)
take away it’s HP cost (135 - (105/2.2)) = 87.3
add the cost of population 87.3+(28*0.2) = 92.9
divide by total power (92.9/40) = 2.32

Now we can calculate the true cost.

True Cost of Damage (TCoD) = Cost + (Power2.32) + (Crew0.2) - (HP/2.2)

Example 1: Cruiser Laser
Cost = 113
Power = 11
Crew = 4
HP = 100

TCoD = 113 + (112.32) + (40.2) - (100/2.2) = 93.87 credit

Example 2: Cruiser Plasma
Cost = 115
Power = 8
Crew = 18
HP = 105

TCoD = 115 + (82.32) + (180.2) - (105/2.2) = 89.42 credit

“Best” Guns’ TCoD

The 6 cruiser guns that are used frequently in competitive plays are

*Cruiser Laser (93.87)
*Cruiser Plasma (89.42)
Multiple Warhead Missiles (MWM) (97.78)
Cruiser Fast Missiles (CFM) (118.34)
Cruiser Beam Laser (CBL) (103.68)
Cruiser Pulse Lasers (CPL) (95.38)

Using Linear Trend Line

[b]**Basic assumptions

  1. A weapon’s damage should have a negative linear relationship with it’s range.
  2. Under rational decisions making, only the best guns get used[/b]

Skip this chapter if you do not believe these.

The purpose of a linear trend line is NOT to determine the variable of any individual cases. Rather it is use to show the general direction of where points should be.

While any weapon can be designed to have damage below or above the trend line, a valid reason should be present to warrant this adjustment. So for example, a weapon might have a 20% penalty from the trend line because it is a dual role weapon.

As I said in many posts, I do not believe in overly complex functions or multiple functions. Complexity obscure biased, while simplicity reveals them. Adjust from the trend line case by case allows the modder to see clearly when and why they make the change.

This specific trend line is derived by drawing a strait line from Cruiser Laser and Cruiser Plasma. Those two weapons are chosen because they

  1. Are the best single role/non missile guns in the game
  2. Accounts for vast majority of single role/non missile guns used.

The line must be drawn across the best guns because guns falling below the best will not get used.

To prevent very high damage at very low range, a solid cap has been place on 0.45 damage per credit.

Trend Line Function

Key
Damage Rating = 1000*(damage/fire interval)

Function
Power = 0.904 - 0.00083Range
If Power > 0.55, then Power = 0.55
Damage Rating = PowerTCoD

Trend Line Implications

Now that we draw a line between CL and Plasma, let’s look at how other weapons fit

Beam Laser
Damage = 21.11
Trend Line Prediction 27.16
Difference 22.27%

Based on Beam Laser, we know that an Anti Tank/Anti Frigate gun will be used with 22.27% penalty from the Trend Line.

Pulse Laser
Damage = 20
Trend Line Prediction 38.51
Difference 48.07%

Based on Pulse Laser, we know that an Anti Frigate/Anti Fighter/Anti AA Armor gun will be used with 48.07% penalty from the Trend Line.

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Hull Bonus (cost, power, hull)

Assumption: The balance cost for HP remains at 2.2 HP/credit. While this is not true for a vastly overpowered race, it works well for balancing toward the original 4.

3 hull bonus affects total damage of a fleet, they are

Cost
Power
HP

It is strongly advise that you use a spreadsheet program (such as excel) to deal with these calculations

Cost

Cost is not as strait forward as it seems. A cost reduction affects damage in 3 ways

Decrease the cost of Crew
Decrease the cost of Power
Decrease the cost of Damage before adjusting for Power/Crew

Intuitive this means if you reduce cost by 1/2, you get not only double base damage, but double HP. So if we assumes the marginal utility of HP remains at 2.2 HP/credit, then the TCoD will drop much greater then 1/2 (Down to around 20%).

Adjusted Cost of Crew (ACoC)
ACoC = (50*Cost Bonus - (75/2.2))/80
ACoC minimum caps at 0

Adjusted Cost of Power (ACoP)
ACoP = (135Cost Bonus - (105/2.2)+(28ACoC))/40
ACoP minimum caps at 0

Adjusted Cost of Damage (ACoD)

ACoD = CostCost Bonus + (PowerACoP) + (Crew*ACoC) - (HP/2.2)

Hull

Assuming the marginal utility of HP remains at 2.2 HP/cost, HP increase damage by doing the following

Decrease the cost of Crew
Decrease the cost of Power
Decrease the cost of Damage before adjusting for Power/Crew

Adjusted Cost of Crew (ACoC)
ACoC = (50 - (75*HP bonus/2.2))/80
At 46.7% HP bonus, the cost of crew becomes 0 as the extra HP from the micro crew alone is enough to justify it’s use, so anything above 46.7% HP bonus means crew cost = 0.
Note - Yes I do spam micro crews on Tribe

Adjusted Cost of Power (ACoP)
ACoP = (135 - ((105HP bonus)/2.2)+(28ACoC))/40

Adjusted Cost of Damage (ACoD)

ACoD = Cost + (PowerACoP) + (CrewACoC) - (HP*HP Bonus/2.2)

This means that for Tribe, the TCoD of a cruiser laser drops from 93.87 to 34.5. No wonder they can just skip defense and win by outgunning everyone.

Power

A power bonus increases your damage by reducing the total cost of a gun, thereby increasing the total amount of guns.

ACoD = Cost + (PowerCoP/Power Bonus) + (CrewCoC) - (HP/2.2)

So suppose a hull with power boost of 50%, the ACoD of Beam Laser will drop to 92.07

Combining the 3

Here are the functions that combines Cost, HP, and Power to show it’s affects on TCoP.

Adjusted Cost of Crew (ACoC)
ACoC = (50Cost Bonus - (75HP Bonus/2.2))/80
ACoC minimum caps at 0

Adjusted Cost of Power (ACoP)
ACoP = (135Cost Bonus - (105HP Bonus/2.2)+(28*ACoC))/40
ACoP minimum caps at 0

Adjusted Cost of Damage (ACoD)

ACoD = CostCost Bonus + (PowerACoP/Power Bonus) + (CrewACoC) - (HPHP Bonus/2.2)

If ACoD drops below 0, it means that the HP from weapon > 2.2 HP/credit, thus you would buy it to boost HP even if it deal no damage.

In practice It doesn’t mean you will still want to buy HP at 2.2 HP/credits, certainly no one buys HP at that price as Tribe. It just means the mod is vastly overpowered.

Implications

Hull Boost does not cancel out with Cost boost. A cost reduction of 1/2 cannot be made up for with 1/2 HP. Because this means you can purchase the same amount of HP at the same price, and your damage increase by 2x. The TCoD Balance for a -50% hull is a -20% cost. Though the hull boost also affects HP of other modules (such as engine) which might warrant a cost reduction around 30%.

Power Boost offers very little cost reduction to a ship, even for a ship that primary uses Beam Laser.

Tribe is OP.

To be continued.

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That took ALOT of work, good job!

Could your next post line up the original weapons into these categories (even a single example per category) to illustrate your point.

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I have included the weapons which are used the most to it’s associated categories. Pay special attention to the blanks since they represents the possibility of new weapon type.

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This is awesome, thanks! I think I will try to use this as inspiration for a balance formula, it seems that may be your ultimate goal here?

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you are the chosen one. the one that shall bring ballance to the fo- err… mods.

:smiley:

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Actually the function was more like a trendline. While points in general should follow that direction, It should not be followed in any strict ways.

Later on I will combine the type with the function later, and show why some condition requires weapon to vary from the trendline. So for example, Dual Role weapons should obviously have reduced damage compare to single role weapons. Anti fighters should also have reduced damage because having them at 490 range doesn’t mean they should deal cruiser laser damage.

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Ok, the categorization of the weapons is simply awesome. I think all modders are going to use this as their ‘Balance Bible’ :smiley:

However I can’t really get the formula. Its logic, or maybe simply the way to use it properly, evades me. [You can see the results of the formula, column Q here. It’s Balance Mod data, but major weapons are unaffected]

The following points are bugging me :

  1. Everything else being equal, long range is better than short range. So i don’t get the fact that higher range reduce DR.
  2. Because of that, the game’s best overall weapon gets negative DR [MWM DR = - 8.4]
  3. The formula doesn’t include damage per interval at all ?

Intuition : the formula you have is constrained by the inputs you have used (cruiser laser & plasma). Using two other weapons as inputs would yield a different formula. I guess.

EDIT : Added (column R) 123stw’s categorization of weapons to the spreadsheet. Just because it’s cool :smiley:

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DR = 1000*(damage/fire interval).
Power = (1000/cost)*(damage/fire interval)

They are only terms representing how much damage they deal per time interval, not how “powerful” they are.

And why CL and Plasma? Because they are both good shieldbreakers at roughly the same cost. It’s pointless to draw a line to light plasma or quantum blast because they are complete crap.

I will change the wording to better communicate the intent.

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It might be a good idea to segregate the weapon types and do a fit against a lot more data points per category. Attempting to work with three or four variables based on two data points makes the mathematician in me… twitchy.

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Section has been clean up to better reflect the intent.

I am not saying they “are” linear, I am saying they “should” be linear. Assuming that only the best weapons get used, then the trend line needs to be drawn through the 2 best weapons in the game. Anything that falls below the linear function without a good reason are useless.

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I found this guide extremely useful, THX!!! :smiley: :smiley:

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Ok, today my brain has mostly recovered, and everything starts to make sense.

As i understand, the DR formula you propose gives an indication of what should be the weapon power, based on its range & cost. Then, using a discretionary approach, we can decide that the actual DPS of the weapon should be above / below the value suggested by the trendline.

Am i correct ?

Then there is just one detail that troubles me.

When range is above 1071 (0.75/0.0007), the trendline gives a negative DR. As some of the game’s useful weapons (missiles) are above this range, they can’t be assessed using that trendline. Suggestions :

  1. Give a lower cap to DR (as you did for low ranges)
  2. Create a different function for long range weapons <— probably a better solution, as long range weapons follow different dynamics

Very true & very important, so i simply wanted to emphasize it.

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I’m not questioning the linear relationship (though it might also be worth looking at a logistic function). What I’m questioning is the fitting against only two data points. If you believe that those two are the perfect model weapons then you may be able to justify it, but I’d still like to see a plot of all the vanilla weapons to see exactly where those weapons lay in relation to others.

I’m trying not to be harsh here, but I don’t think a mathematician would let you get away with a sentence about revealing bias and then go on to make a line fit on two data points, for two reasons:

  1. Hand-picking a couple of points out of many and then fitting to them is the ultimate bias.
  2. A line fit on two points won’t generally be considered to be valid.

Please don’t take this as me just criticising you. I would like to see a method like this end up working out to make modders’ lives easier, but I’d also like to see it done in a way that will stand up to scrutiny :slight_smile:

14

Assume usage in a competitive environment reflects effectiveness and balance. Samples should be drawn from competitive online play.

Sampling from all SAC/NEC suggest that the only cruiser weapons used at a significant level are

Cruiser Laser
Cruiser Plasma
MWM
Beam Lasers
Pulse Lasers
maybe Fast Missiles on small maps.

Now, there are no unbiased ways to accurately depict missile damage compare to others, since they use a completely different mechanics. Beam laser falls 3 DR short but is a Dual Roles (anti tank anti frigate) so the 15% reduction still warrant it’s use. Not to mention that Beam Laser really goes into style after the mass introduction of armor tanks. Pulse laser has always been the “anti fighter gun that isn’t completely useless outside of context”, that thing is borderline 3 Roles.

So if you gather samples on single role non missile weapons from competitive online challenges, you will end up with Cruiser Laser and Cruiser Plasma.

The assumption that rational people will only use the best guns in the game seem to hold well with empirical evidence.

Again, other guns are not added because they don’t get used, indicating that they are useless and not balanced. If there is another single role non missile weapon that are used I would have included it. This is not about equal representation of each gun, it’s about identifying which guns are the best and draw a line through them.

Put it in another way, if you balance your mod base on a line lower than the CL/Plasma line, your mod will get crushed by the typical CL/Plasma spams.

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That all makes sense and now I can see where you’re coming from. I’d still like to see where the used weapons lay with respect to the others though. It may be good to establish a lower bound for DR, below which you can guarantee that no one will pick that weapon even if they save on crew and power. I’ll have a go at knocking up a scatterplot of DR versus range, highlighting the popular weapons. Maybe there’s some other trends in there that we can spot as well.

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The hardest thing about writing a function is that, as mention before, only those 6 weapons see much plays, and 2 of them are missiles… Maybe you can squeeze in the 3 race specific weapons (Nomad missiles, Swarm Disruptor, Rad Gun), but even that is not enough empirical evidence to suggest balance in any way. The only reason I accept the negative correlation is because short range requires more engines to deliver the damage. Play test shows that long range needs < 0.1 speed, mid range needs around 0.2 speed, close range needs around 0.3 speed.

Making a linear relationship for missile doesn’t seem to make any sense. Too many situational stats (tracking, fuel, decoy, move speed, huge variation in damage to range) makes quantifying them unreliable. A comparison between MWM and Fast missile is like comparing 2 extremes. The MWM is all damage and range, the Fast missile has terrible paper damage by comparison when adjusted for range, but it has tracking, move speed, and reduced fuel to make them work.

The whole “mid range shield breaker” is an whole field that is completely untouched. The trend line suggest to give them 20 to 30 DR, but until a weapon like that is implemented we won’t know how it alters the playing field.

Maybe the trend line should be use to determine damage of the 3 range bracket. It’s not like you need more engines to go from 490 range to 100 range. So long as your ships can dodge the plasma it’s the same.

17

Something interesting comes out of the C4 plasmas - all of the cruiser plasma weapons have almost identical DR values. In fact, the cruiser plasma and cruiser heavy plasma are the closest. Plasma has range 950 and DR 10, heavy plasma has range 900 and DR 10. For the 50 drop in range you gain 3 armour penetration and 11 shield penetration.

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Which is particularly why the other 2 never see the light of day. And why only the Cruiser Plasma gets used.

shield penetration beyond 27 is the same, so we can just ignore that.

For heavy plasma, 3 armor penetration, and 6 less crews, while attractive, is being weighted against -1/3 tracking, -50 range, +30 weight, +2 power.

Light plasma is just beyond pathetic. To make them useful their fire interval needs to be cut by 1/2. Even then they won’t be the sharpest knife in the drawer.

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Added “True Cost of Damage” and adjusted the trend line equation accordingly.

This new trend line takes into account power/crew cost of a weapon.

20

Excellent. I tried to do that on my own yesterday, but wasn’t too satisfied with the result. I hadn’t thought about correcting the HP effect in power & crew. It’s much better this way. I really like the method used to estimate the cost of one HP, it’s very ‘clean’.